%0 Journal Article
%T Isometries on extremely non-complex Banach spaces
%A Piotr Koszmider
%A Miguel Martin
%A Javier Meri
%J Mathematics
%D 2009
%I arXiv
%X Given a separable Banach space $E$, we construct an extremely non-complex Banach space (i.e. a space satisfying that $\|Id + T^2\|=1+\|T^2\|$ for every bounded linear operator $T$ on it) whose dual contains $E^*$ as an $L$-summand. We also study surjective isometries on extremely non-complex Banach spaces and construct an example of a real Banach space whose group of surjective isometries reduces to $\pm Id$, but the group of surjective isometries of its dual contains the group of isometries of a separable infinite-dimensional Hilbert space as a subgroup.
%U http://arxiv.org/abs/0901.1512v2